For the subcritical case \(\alpha >1\)  we can adopt [1]}. To get the model to satisfy its assumptions, we use a cut-off function \(\chi (z)\)  and small \(\varepsilon >0\)  to break the residual term \(G\)  further into inner singular part
\(G_\varepsilon = \frac{h(z)\chi (z/\varepsilon )}{|z|^{n+\alpha }}\left[\frac{\rho _0(x+z)}{\left(_{\Omega (0,z)}\rho _0(x+\xi )\, \mbox{d}\xi \right)^{\frac{\tau }{n}}} - \frac{\rho _0(x)}{\rho _0(x)^{\frac{\tau }{n}}}\right],\) 
